If y= ⁻¹ [ 1+ x + 1- x 1+ x - 1- x ] , where 0 x 2 , then d y d x is equal to

Step-by-step solution

aligned & y= ⁻¹ [ 1+ x + 1- x 1+ x - 1- x ] aligned aligned & y= ⁻¹ [ ( x 2 + x 2 )^2 + ( x 2 - x 2 )^2 ( x 2 + x 2 )^2 - ( x 2 - x 2 )^2 ] aligned aligned & y= ⁻¹ [ x 2 + x 2 + x 2 - x 2 x 2 + x 2 - x 2 + x 2 ] & y = ⁻¹ [ 2 x 2 2 x 2 ]= ⁻¹ ( x 2 )= x 2 & dy dx = 1 2 aligned